Turbulence and Coarsening in Active and Passive Binary Mixtures

Berti, Stefano; Boffetta, G.; Cencini, Massimo; Vulpiani, Angelo

doi:10.1103/physrevlett.95.224501

Cited by 50 publications

(70 citation statements)

References 30 publications

(58 reference statements)

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“…Under uniform shear flow, a highly anisotropic layered phase ordering appears in the mixture [7][8][9]. Under turbulent flow, experiments [10,11] and numerical simulations [12,13] have shown that coarsening is suppressed due to vigorous stirring, a result that is also observed when a chaotic flow is imposed [14].…”

Section: Introductionmentioning

confidence: 65%

“…In this case, the Navier-Stokes equations contain a capillary term that embodies gradients in chemical potential, and thereby a feedback from the phase-evolution equation. This term alone, however, is insufficient to suppress coarsening-on the contrary, the main observation is that, in an unstirred fluid, domain growth of the phase-separating field is enhanced [12].…”

Section: Introductionmentioning

confidence: 91%

“…The paradigmatic model used to investigate this process is the advective Cahn-Hilliard equation coupled to the incompressible Navier-Stokes equations [12][13][14][15]. In this case, the Navier-Stokes equations contain a capillary term that embodies gradients in chemical potential, and thereby a feedback from the phase-evolution equation.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Cueto‐Felgueroso

Juanes

2016

Phys. Rev. E

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We study the evolution of binary mixtures far from equilibrium, and show that the interplay between phase separation and hydrodynamic instability can arrest the Ostwald ripening process characteristic of nonflowing mixtures. We describe a model binary system in a Hele-Shaw cell using a phase-field approach with explicit dependence of both phase fraction and mass concentration. When the viscosity contrast between phases is large (as is the case for gas and liquid phases), an imposed background flow leads to viscous fingering, phase branching, and pinch off. This dynamic flow disorder limits phase growth and arrests thermodynamic coarsening. As a result, the system reaches a regime of statistical steady state in which the binary mixture is permanently driven away from equilibrium.

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Section: Introductionmentioning

confidence: 65%

Section: Introductionmentioning

confidence: 91%

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Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Cueto‐Felgueroso

Juanes

2016

Phys. Rev. E

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“…The blob size grows as L ∼ t 2/3 if unforced [21]. The length scale growth can be arrested by external fluid forcing, and an emergent characteristic length scale of the blob size is formed by the critical balance between turbulent kinetic energy and surface tension energy in 2D CHNS turbulence [22]. In three dimensions, the length scale growth is also arrested when proper …”

Section: Introductionmentioning

confidence: 99%

“…This exponent can be obtained dimensionally by balancing the advection term v · ∇ω and the surface tension force term ξ 2 ρ B ψ · ∇∇ 2 ψ in Eq. (2) forcing can arrest the length scale growth [22]. Larger forcing leads to a larger enstrophy dissipation rate ϵ , and thus a smaller Hinze scale.…”

Section: B Benchmarkmentioning

confidence: 99%

Cascades and spectra of a turbulent spinodal decomposition in two-dimensional symmetric binary liquid mixtures

et al. 2016

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We study the fundamental physics of cascades and spectra in two-dimensional (2D) Cahn-Hilliard-Navier-Stokes (CHNS) turbulence, and compare and contrast this system with 2D magnetohydrodynamic (MHD) turbulence. The important similarities include basic equations, ideal quadratic invariants, cascades, and the role of linear elastic waves. Surface tension induces elasticity, and the balance between surface tension energy and turbulent kinetic energy determines a length scale (Hinze scale) of the system. The Hinze scale may be thought of as the scale of emergent critical balance between fluid straining and elastic restoring forces. The scales between the Hinze scale and dissipation scale constitute the elastic range of the 2D CHNS system. By direct numerical simulation, we find that in the elastic range, the mean square concentration spectrum H ψ k of the 2D CHNS system exhibits the same power law (−7/3) as the mean square magnetic potential spectrum H A k in the inverse cascade regime of 2D MHD. This power law is consistent with an inverse cascade of H ψ , which is observed. The kinetic energy spectrum of the 2D CHNS system is E K k ∼ k −3 if forced at large scale, suggestive of the direct enstrophy cascade power law of 2D Navier-Stokes turbulence. The difference from the energy spectra of 2D MHD turbulence implies that the back reaction of the concentration field to fluid motion is limited. We suggest this is because the surface tension back reaction is significant only in the interfacial regions. The interfacial regions fill only a small portion of the 2D CHNS system, and their interface packing fraction is much smaller than that for 2D MHD.

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On a Regularized Family of Models for Homogeneous Incompressible Two-Phase Flows

Gal

Medjo

2014

J Nonlinear Sci

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Abstract. We consider a general family of regularized models for incompressible two-phase flows based on the Allen-Cahn formulation in n-dimensional compact Riemannian manifolds for n = 2, 3. The system we consider consists of a regularized family of Navier-Stokes equations (including the Navier-Stokes-α-like model, the Leray-α model, the Modified Leray-α model, the Simplified Bardina model, the Navier-Stokes-Voight model and the Navier-Stokes model) for the fluid velocity u suitably coupled with a convective Allen-Cahn equation for the order (phase) parameter φ. We give a unified analysis of the entire three-parameter family of twophase models using only abstract mapping properties of the principal dissipation and smoothing operators, and then use assumptions about the specific form of the parameterizations, leading to specific models, only when necessary to obtain the sharpest results. We establish existence, stability and regularity results, and some results for singular perturbations, which as special cases include the inviscid limit of viscous models and the α → 0 limit in α-models. Then, we also show the existence of a global attractor and exponential attractor for our general model, and then establish precise conditions under which each trajectory (u, φ) converges to a single equilibrium by means of a Lojasiewicz-Simon inequality. We also derive new results on the existence of global and exponential attractors for the regularized family of Navier-Stokes equations and magnetohydrodynamics models which improve and complement the results of [44]. Finally, our analysis is applied to certain regularized Ericksen-Leslie (RSEL) models for the hydrodynamics of liquid crystals in n-dimensional compact Riemannian manifolds.

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Turbulence and Coarsening in Active and Passive Binary Mixtures

Cited by 50 publications

References 30 publications

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Thermodynamic coarsening arrested by viscous fingering in partially miscible binary mixtures

Cascades and spectra of a turbulent spinodal decomposition in two-dimensional symmetric binary liquid mixtures

On a Regularized Family of Models for Homogeneous Incompressible Two-Phase Flows

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